There are exactly three points, representing two straight lines with a distance of 1 from the straight line L, one tangent to the circle and the other intersecting the circle.

Center (0,0), radius 2

The distance from a straight line tangent to the circle to the center of the circle is 2. Move the distance to the center of the circle by 1 to get a straight line L, so the distance from L to the center of the circle is 2- 1= 1.

Then, the distance formula from point to straight line is used to obtain:

Solution: b= root 2 or b=- root 2.